空间几何问题解决过程中工作记忆资源分配策略的个体差异
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摘要
本文以某中学高二数学学优生15名和数学学困生15名为被试，以两道高考数学北京试卷中的立体几何题目的解题过程为实验材料，对中学生工作记忆资源分配策略进行了考察；着重研究了认知负荷对中学生空间问题解决过程中工作记忆资源分配策略的影响，实验结果表明：(1)随着认知负荷的增大，两组被试首次内部思考时间都呈现增加的趋势，但是在解答简单题时，学优生与学困生的首次内部思考时间没有显著差异；在解答中等题和难题时，学优生趋向于在较短时间内使用首次内部思考策略，而学困生则倾向于在较长时间内使用首次内部思考策略。(2)随着认知负荷的增大，两组被试在解题过程中使用外部策略的总频数呈现不同的特点，学优生使用外部策略的总频数的平均值呈增加的趋势，分别是9次，11次和20次，能够适当的增加外部策略的使用来分配认知负荷强度，而学困生的相应数据分别22次、20次和10次，呈下降的趋势，表现为在简单题、中等题上使用过多的外部策略；(3)随着认知负荷的增大，学优生在解题过程中用于内部思考时间的比率总体呈现降低的趋势，即内部思考策略所用时间占整个解题时间的比率随认知负荷的加大而减少，但是学困生则相反；(4)随着认知负荷的增大，学优生和学困生的内外部策略转换系数都在减小，这表明，无论是学优生还是学困生，工作记忆资源分配策略的选择和应用受到了认知负荷的影响。但是无论是简单题、中等题还是难题，学优生的内外策略转换系数均显著高于学困生。这表明：学优生可以更合理地使用工作记忆资源。
Experiment was conducted among 15 students from the advanced group and another 15 from the less advanced group of Senior Two of a certain high school. The experiment materials were taken from the resolving process of several solid geometry exercises in the mathematic exam papers for higher education entrance examination of Beijing City. The experiment surveyed the distribution strategy of the work memory resources in the process of solving the exercises of space geometry. The study focused on the impact of cognition load toward distribution strategy of the work memory resources in the process of solving the exercises of space geometry, in the course of which it also showed concern on the individual difference of each data target. The experiment results showed that: (1) Along with the increase of cognition load, the two experiment groups had an upward tendency in the time of initial inner thinking. However, in solving the simpler problems, there were no significant difference between the advanced group and the less advanced group in the time of initial inner thinking. In solving questions of average difficulty and top difficulty, the advanced group tends to use initial inner thinking strategy within a shorter period of time, whereas the less advanced group longer. (2) Along with the increases of cognition load, the two groups had different features in using the external strategy in the course of problem-solving. The average value of advanced group using the external strategies tends upward, respectively 9, 11 and 20 times, capable of increasing external strategy to allocate the intensity of cognition load, whereas the data of the less advanced group are respectively 22, 20 and 10 times, showing an downward tendency, which displayed over use of external strategies in solving simpler and average problems. (3) Along with the increases of the cognition load, the advanced group had a downward tendency in using the inner thinking time in the course of problem-solving, i.e. the time used in inner
Experiment was conducted among 15 students from the advanced group and another 15 from the less advanced group of Senior Two of a certain high school. The experiment materials were taken from the resolving process of several solid geometry exercises in the mathematic exam papers for higher education entrance examination of Beijing City. The experiment surveyed the distribution strategy of the work memory resources in the process of solving the exercises of space geometry. The study focused on the impact of cognition load toward distribution strategy of the work memory resources in the process of solving the exercises of space geometry, in the course of which it also showed concern on the individual difference of each data target. The experiment results showed that: (1) Along with the increase of cognition load, the two experiment groups had an upward tendency in the time of initial inner thinking. However, in solving the simpler problems, there were no significant difference between the advanced group and the less advanced group in the time of initial inner thinking. In solving questions of average difficulty and top difficulty, the advanced group tends to use initial inner thinking strategy within a shorter period of time, whereas the less advanced group longer. (2) Along with the increases of cognition load, the two groups had different features in using the external strategy in the course of problem-solving. The average value of advanced group using the external strategies tends upward, respectively 9, 11 and 20 times, capable of increasing external strategy to allocate the intensity of cognition load, whereas the data of the less advanced group are respectively 22, 20 and 10 times, showing an downward tendency, which displayed over use of external strategies in solving simpler and average problems. (3) Along with the increases of the cognition load, the advanced group had a downward tendency in using the inner thinking time in the course of problem-solving, i.e. the time used in inner
引文
1 杨治良，郭力平，王沛，陈宁．记忆心理学．第二版．上海：华东师范大学出版社，2004．
2 朱智贤．心理学大词典．北京：北京师范大学出版社，1989．
3 曹宝龙，刘慧娟，林崇德．认知负荷对小学生工作记忆资源分配策略的影响心理发展与教育，2005，1：36-42．
4 梁好翠．几何学习能力感、学习策略与几何学习成绩关系的研究．抚州师专学报，2000，6：97-103．
5 李毅侠．高中生数学学习策略调查研究．教学与管理，2001，8：38-40．
6 刘慧娟，沃建中．中学生连环数运算中的工作记忆资源分配策略心理发展与教育，2003，4：39-45．
7 王春艳，韩雪．数学学习态度、学习策略对学生学习成绩的影响研究长春师范学院学报，2004，3：87-90．
8 许洁英．个体差异研究及其教学意义西北师大学报，社会科学版，1999，11：20-24．
9 张庆林，连庸华．优等生解决几何问题的成功思维策略分析．西南师范大学学报，2005，1：19-23．
10 周珍，连四清，周春荔．中学生空间图形认知能力的发展与数学成绩的关系及其与智力的相关性研究．数学教育学报，2001，2：12-16．
11 Weinstein，C．E．，&Hume，L．M．．终身受用的学习策略．伍新春，秦宪刚译．中国轻工业出版社，2003．
12 Bray, N. W., Reilly, K. D., VilIa, M. F., & Grupe, L. A.. Neural network models and mechanisms of strategy development. Developmental Review, 1997, 17: 525-566.
13 Cary, M., & Carlson, R. A.. External support and the development of problem solving routines, Journal of experimental psychology: Learning, Memory, and Cognition, 1999, 25(4): 1053-1070.
14 Cary, M., & Carlson, R. A.. Distributing working memory resources during problem solving, Journal of experimental psychology: Learning, Memory, and Cognition, 2001, 27(3): 836-848.
15 Carlson, R. A., Wenger, J.L., & Sullivan, M. A.. Coordinating information from perception and working memory. Journal of Experimental Psychology: Human perception and performance, 1993,19: 531-548.
16 Geary, D. C. A componential analysis of an early learning deficit in mathematics, Journal of Experimental Child Psychology, 1990,49: 363-383.
17 Hitch, G. J., & McAuley, E.. Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 1990, 82: 375-386.
18 Swanson H. L.. Effects of cognitive effort and word distinctiveness on learning disabled reader's recall. Journal of Education Psychology, 1984,76: 894-908.
19 Swanson, H. L., & Sachse, L.C.. Learning disabled readers' working memory: What does or does not develop? Unpublished manuscript, University of California, 2001, 30: 345-365.
20 Sweller, J., van Merri(?)nboer, J. J. G., & Paas, F. G. W. C.. Cognitive architecture and instructional design. Educational Psychology Review, 1998,10(3): 251-296.
2 朱智贤．心理学大词典．北京：北京师范大学出版社，1989．
3 曹宝龙，刘慧娟，林崇德．认知负荷对小学生工作记忆资源分配策略的影响心理发展与教育，2005，1：36-42．
4 梁好翠．几何学习能力感、学习策略与几何学习成绩关系的研究．抚州师专学报，2000，6：97-103．
5 李毅侠．高中生数学学习策略调查研究．教学与管理，2001，8：38-40．
6 刘慧娟，沃建中．中学生连环数运算中的工作记忆资源分配策略心理发展与教育，2003，4：39-45．
7 王春艳，韩雪．数学学习态度、学习策略对学生学习成绩的影响研究长春师范学院学报，2004，3：87-90．
8 许洁英．个体差异研究及其教学意义西北师大学报，社会科学版，1999，11：20-24．
9 张庆林，连庸华．优等生解决几何问题的成功思维策略分析．西南师范大学学报，2005，1：19-23．
10 周珍，连四清，周春荔．中学生空间图形认知能力的发展与数学成绩的关系及其与智力的相关性研究．数学教育学报，2001，2：12-16．
11 Weinstein，C．E．，&Hume，L．M．．终身受用的学习策略．伍新春，秦宪刚译．中国轻工业出版社，2003．
12 Bray, N. W., Reilly, K. D., VilIa, M. F., & Grupe, L. A.. Neural network models and mechanisms of strategy development. Developmental Review, 1997, 17: 525-566.
13 Cary, M., & Carlson, R. A.. External support and the development of problem solving routines, Journal of experimental psychology: Learning, Memory, and Cognition, 1999, 25(4): 1053-1070.
14 Cary, M., & Carlson, R. A.. Distributing working memory resources during problem solving, Journal of experimental psychology: Learning, Memory, and Cognition, 2001, 27(3): 836-848.
15 Carlson, R. A., Wenger, J.L., & Sullivan, M. A.. Coordinating information from perception and working memory. Journal of Experimental Psychology: Human perception and performance, 1993,19: 531-548.
16 Geary, D. C. A componential analysis of an early learning deficit in mathematics, Journal of Experimental Child Psychology, 1990,49: 363-383.
17 Hitch, G. J., & McAuley, E.. Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 1990, 82: 375-386.
18 Swanson H. L.. Effects of cognitive effort and word distinctiveness on learning disabled reader's recall. Journal of Education Psychology, 1984,76: 894-908.
19 Swanson, H. L., & Sachse, L.C.. Learning disabled readers' working memory: What does or does not develop? Unpublished manuscript, University of California, 2001, 30: 345-365.
20 Sweller, J., van Merri(?)nboer, J. J. G., & Paas, F. G. W. C.. Cognitive architecture and instructional design. Educational Psychology Review, 1998,10(3): 251-296.